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Documents authored by Kavvos, G. A.

Document
DOI: 10.4230/LIPIcs.FSCD.2026.20
Relational Dualities and Bisimulation

Authors: Piotr Kozicki and G. A. Kavvos

Published in: LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)

Abstract
The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational systems (e.g. the states of a machine), the corresponding algebra is one of logical predicates on these systems (e.g. predicates on these states, i.e. program logics). Our aim is to extend this phenomenon to relations, putting well-behaved relations between systems (e.g. bisimulations) in correspondence with relations between predicates. This is achieved by constructing particular relational extensions of Tarski duality (for infinitary classical propositional logic) and Thomason duality (for infinitary classical modal logic). We sketch how these dualities give rise to a proof system that relates formulae between different systems.
Cite as

Piotr Kozicki and G. A. Kavvos. Relational Dualities and Bisimulation. In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kozicki_et_al:LIPIcs.FSCD.2026.20,
  author =	{Kozicki, Piotr and Kavvos, G. A.},
  title =	{{Relational Dualities and Bisimulation}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.20},
  URN =		{urn:nbn:de:0030-drops-263703},
  doi =		{10.4230/LIPIcs.FSCD.2026.20},
  annote =	{Keywords: bisimulation, modal logic, duality, categorical semantics}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.14
Two-Dimensional Kripke Semantics I: Presheaves

Authors: G. A. Kavvos

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
The study of modal logic has witnessed tremendous development following the introduction of Kripke semantics. However, recent developments in programming languages and type theory have led to a second way of studying modalities, namely through their categorical semantics. We show how the two correspond.
Cite as

G. A. Kavvos. Two-Dimensional Kripke Semantics I: Presheaves. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 14:1-14:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kavvos:LIPIcs.FSCD.2024.14,
  author =	{Kavvos, G. A.},
  title =	{{Two-Dimensional Kripke Semantics I: Presheaves}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{14:1--14:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.14},
  URN =		{urn:nbn:de:0030-drops-203438},
  doi =		{10.4230/LIPIcs.FSCD.2024.14},
  annote =	{Keywords: modal logic, categorical semantics, Kripke semantics, duality, open maps}
}
Document
DOI: 10.4230/LIPIcs.ITP.2022.28
Deeper Shallow Embeddings

Authors: Jacob Prinz, G. A. Kavvos, and Leonidas Lampropoulos

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)

Abstract
Deep and shallow embeddings are two popular techniques for embedding a language in a host language with complementary strengths and weaknesses. In a deep embedding, embedded constructs are defined as data in the host: this allows for syntax manipulation and facilitates metatheoretic reasoning, but is challenging to implement - especially in the case of dependently typed embedded languages. In a shallow embedding, by contrast, constructs are encoded using features of the host: this makes them quite straightforward to implement, but limits their use in practice. In this paper, we attempt to bridge the gap between the two, by presenting a general technique for extending a shallow embedding of a type theory with a deep embedding of its typing derivations. Such embeddings are almost as straightforward to implement as shallow ones, but come with capabilities traditionally associated with deep ones. We demonstrate these increased capabilities in a number of case studies; including a DSL that only holds affine terms, and a dependently typed core language with computational beta reduction that leverages function extensionality.
Cite as

Jacob Prinz, G. A. Kavvos, and Leonidas Lampropoulos. Deeper Shallow Embeddings. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{prinz_et_al:LIPIcs.ITP.2022.28,
  author =	{Prinz, Jacob and Kavvos, G. A. and Lampropoulos, Leonidas},
  title =	{{Deeper Shallow Embeddings}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.28},
  URN =		{urn:nbn:de:0030-drops-167379},
  doi =		{10.4230/LIPIcs.ITP.2022.28},
  annote =	{Keywords: type theory, shallow embedding, deep embedding, Agda}
}
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